Cox had 22 tackles in six games for the Jaguars this season.
The third-year pro out of William & Mary has 143 tackles and eight interceptions in 35 career contests for Jacksonville.
LeFevour was a sixth-round draft pick of the Chicago Bears in 2010. He was claimed off waivers by Cincinnati that September and spent the entire season on the 53-man roster, though he was inactive for all 16 games.
The 6-foot-3, 230-pounder was most recently signed to the Colts practice squad.
LeFevour was a four-year starter at Central Michigan, where he passed for 12,905 yards with 102 touchdowns and 35 interceptions. He added 2,948 rushing yards and 47 touchdowns. His 150 total touchdowns are the most in the NCAA Bowl Subdivision.